Abstract
Primordially a geometry was a science on properties of geometrical objects and their mutual disposition. A use of the proper Euclidean geometry generated the axiomatic conception of geometry, where the geometry is considered as a logical construction. There is the metrical conception of a geometry, where the geometry is considered as a science on properties of geometric objects. In the framework of metrical conception the space-time geometries form a more powerful set of geometries, than those do in the framework of the axiomatic conception. It is important at the construction of the general relativity.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Blumenthal, L.M.: Theory and Applications of Distance Geometry. Clarendon Press, Oxford (1953)
Rylov, Y.A.: Geometry without topology as a new conception of geometry. Int. Jour. Mat. & Mat. Sci. 30 (12), 733–760 (2002). arXiv: math.MG/0103002
Rylov, Y.A.: General relativity extended to non-Riemannian space-time geometry. e-print/0910.3582v7
Rylov, Yu. A.: Induced antigravitation in the extended general relativity, Vol. 18, pp 107–112 (2012)
Rylov, Y.A.: Tachyon gas as a candidate for dark matter, Vestnik RUDN ser. Math. Inform. Phys. iss 2 pp.159-173 (In Russian) (2013)
Rylov, Y.A.: Dynamic equations for tachyon gas. Int. J. Theor. Phys. 52 (133(10)), 3683–3695 (2013)
Rylov, Y.A.: Logical reloading. What is it and what is a profit from it? Int. J. Theor. Phys. doi:10.1007/s10773.014.2039.3
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Rylov, Y.A. Metrical Conception of the Space-Time Geometry. Int J Theor Phys 54, 334–339 (2015). https://doi.org/10.1007/s10773-014-2228-0
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10773-014-2228-0